题目描述
There are N cities on a 2D plane. The coordinate of the i-th city is $(x_i, y_i). Here (x_1, x_2, \dots, x_N)$ and $(y_1, y_2, \dots, y_N)$ are both permuations of $(1, 2, \dots, N)$.
For each $k = 1,2,\dots,N,$ find the answer to the following question:
Rng is in City k. Rng can perform the following move arbitrarily many times:
- move to another city that has a smaller x-coordinate and a smaller y-coordinate, or a larger x-coordinate and a larger y-coordinate, than the city he is currently in.
How many cities (including City k) are reachable from City k?
Constraints
- $1 \leq N \leq 200,000$
- $(x_1, x_2, \dots, x_N)$ is a permutation of $(1, 2, \dots, N)$.
- $(y_1, y_2, \dots, y_N)$ is a permutation of $(1, 2, \dots, N)$.
- All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print N lines. In i-th line print the answer to the question when k = i.
Examples
Input
4
1 4
2 3
3 1
4 2
Output
1
1
2
2
Input
7
6 4
4 3
3 5
7 1
2 7
5 2
1 6
Output
3
3
1
1
2
3
2
输入格式
见题面
输出格式
见题面
样例输入
7
6 4
4 3
3 5
7 1
2 7
5 2
1 6
样例输出
3
3
1
1
2
3
2